Methods for growing crystals of gallium nitride (GaN) and other group III nitride based compound semiconductors through the flux method are disclosed in, for example, the Patent Documents below. In one of these methods, gallium (Ga) is dissolved in molten sodium (Na) at a constant temperature of about 800° C., and gallium is reacted with nitrogen under high pressure of about 100 atm, to thereby grow gallium nitride (GaN) on the surface of a seed crystal. One known apparatus 9000 for producing a group III nitride based compound semiconductor is shown in FIG. 4. The apparatus has an openable/closable double hermetic vessel structure having a reactor 100 and an outer vessel 200, which are resistant to high temperature and pressure. The reactor 100 is heated by means of heating apparatuses 31a, 31b, and 31c disposed in the outer vessel 200, to thereby melt sodium (Na) and gallium (Ga) contained in the reactor 100. To the reactor 100, a nitrogen feed pipe 10 and a discharge pipe 11 are connected. Feeding and discharging nitrogen is carried out, while the internal pressure of the reactor 100 is controlled to, for example, 100 atm, by means of a controller (not illustrated).    [Patent Document 1] Japanese Patent Application Laid-Open (kokai) No. 2001-058900    [Patent Document 2] Japanese Patent Application Laid-Open (kokai) No. 2003-313099
In the flux method, nitrogen gas for enclosing the reaction system also serves as a source for forming GaN, and is consumed as the progress of reaction. Thus, preferably, additional nitrogen is appropriately fed to the reaction system while the pressure of the system is maintained. However, when the additionally fed nitrogen is not heated to a temperature almost equivalent to the temperature of a molten Na—Ga mixture, GaN crystals other than the seed crystal are deposited at random in the surface of the flux. This phenomenon impairs efficiency of production of a thick single-crystal substrate.